My 87 740 non-turbo with 250,000 mi, never any major problems, suddenly wants to stall at times. I drive it 20 miles, mostly highway speed, to work early in the morning every day. About 70 degrees. No problem. Smooth as a sewing machine. But, in the afternoon, 90 plus degrees, it starts fine at work, no problem for several miles on secondary road to Interstate, no problem on Interstate, but when I exit the Interstate after about 15 miles at 70mph and try to start after stopping at the end of the exit ramp, it tries to stall and is rough running for the remainder of the trip home, about a mile with one more traffic light stop. One time it died on me and would not restart immediately. After waiting a few minutes, it started back up and seemed to run OK. My Volvo specialist, not dealer, changed the Fuel Pump and Fuel Filter. Made no difference. He is puzzled and so am I. Anyone have any suggestions as to what might be the trouble?

Try cleaning your throttle body. Worked for me and its cheap. Make sure you use fuel injector cleaner not carb cleaner(too harsh for plastics)
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Have you checked the fuel pump relay? Per the 700/900 FAQ, check under the central console and feel the fuel pump relay to see if it is hot. The relay should not be hot to the touch, if it is, replace the relay. Even if it is not hot, you may want to go ahead and replace the relay anyway if it hasn't ever been replaced. Those relays are notorious for developing micro-cracks in the solder.

Does your car have the distributor at the back of the head? If so it could be the Hall affect device. Does the tach bounce a little when you're cranking the engine? If not that's it. Could be the injector relay. Check to see if the air filter box heated air flap is closing after warmup. Has the engine wireing harnes ever been replaced? The pre 88's have bad wire insulating which tends to crumble over time and cause electrical shorts.